Technical ReportPDF Available

# waves2Foam Manual

Authors:

## Abstract and Figures

This is the draft version of the waves2Foam Manual. It has 'draft' as a descriptor, since some textual editing might still occur. Nonetheless, the manual is covering the full functionality and replaces previous online documentation.
Content may be subject to copyright.
 
F
y z
∂ρu
∂t +∇ · ρuuT=−∇p+g·(xxr)ρ+∇ · µtot u
ρut
= (∂/∂x, ∂/∂y, ∂/∂z)pg
x= (x, y, z)xr
µtot
∇ · u= 0
p=pρg·xp
n
u=nup
up
(1 + Cm)
∂t
ρu
n+1
n∇ · ρ
nuuT=−∇p+g·(xxr)ρ+1
n∇ · µtotuFp
CmFp
F
∂F
∂t +∇ · uF+∇ · ur(1 F)F= 0
urF
ρ=F ρ1+ (1 F)ρ0µ=F µ1+ (1 F)µ0
F= 0
F= 1 F= 1 F= 0
F[0,1]
∂F
∂t +1
n(∇ · uF+∇ · ur(1 F)F) = 0
n
φ= (1 wR)φ+wRφ
wR[0,1]
αu
wR
˜wR= 1 (1 w
R)/max
w
R= 1 wR˜wR
max
wR(σ= 1) = 0 wR(σ= 0) = 1 σ
wR= 1 exp σp1
exp 1 1
p3.5
wR= 1 σp
p
p
wR=σ3+ 3˜σ2
˜σ= 1 σ
Fp
ρ=au+bukuk2
a b Cm
Cm=γp
1n
n
γp0.34
a b
a=α(1 n)3
n2
ν
d2
50
, b =β1n
n3
1
d50
ν d50
a b
a=α(1 n)2
n3
ν
d2
50
, b =β1 + 7.5
KC 1n
n3
1
d50
ν d50
α β KC
KC
3×3 = 9
1
0 1
σ
1
φ3
φρ
φF3
φ φF
φF
φ φρ
φρ= (ρF=1 ρF=0)φF+ρF=0 φ
φF
φF=φρρF=0φ
ρF=1 ρF=0
F= 1
F
q=X
f∈F
φF,f
Sf
kSfk2
q3Sf
φF
φFφ φρ
φF
q
Hm=H01 + sin 1
N(ωt k·x)
HmH0
N ω k
h/L h L
m
1
m m
1
η=
N
X
i
aicos(ωitki·x+ϕi)
η N ai
i ω kϕ
aiωi
ωiϕi
x0t0
0
t= 0
t= 0
x y z
x y z
t= 0
x
kω
k
kω
up
kω
KC
f= 1/Tef
Te
100
R(τ) = 1
m0Z−∞
0
S(f) cos 2πf τ f
R(τ)S(f)f τ
m0
Rd(τ)'1
2md,0
N1
X
n=0
[Sd(fn) cos(2πfnτ) + Sd(fn+1 ) cos(2πfn+1τ)] ∆fn
dfn=fn+1 fnN
η
η(t, x) =
N
X
m=1
amcos (ωmtkm·x+ϕm)
amωmkmx
ϕm[0,2π]
am=p[Sd(fm1) + Sd(fm)]∆fm1
ωm=π(fm+fm1)
τ > 0 cos(2π fnτ)=1
n TrTm01
Tr
fn=nδf0fn=δf0n= 0,1...,N
Tr=1
δf0
=N
fN
fN
N fNTr
fn= (1 + f)δf0
fn=nδf0+αfδf0nn+ 1
21=δf0(n+αfAn)
1/(1 N)< αfαf= 0
cos(2πfnτ) = cos(2πnδf0τ) cos(2παfAnδf0τ)
sin(2πnδf0τ) sin(2παfAnδf0τ)
n
nδf0τ=K αfAnδf0τ=L
K L τ
K
n
L
An
αf= 1
α
τ Rd= 1
αfTrα= 1/4Tr= 1/δf0Tr= 4/δf0
α= 4 αfδf0
δf0αf
Tr
S
fLfPfU
[fL, fP[
NL=fPfL
fUfP (N+ 1)
[fP, fU]NU=N+ 1 NL
fn=fL+ (fPfL) sin 2π
4NL
nn= 0,...NL1
fNL+n=fP+ (fUfP)1cos 2π
4NU
n n= 0,...NU
f f fL= 0.03
fU= 1.4Tp= 3 N= 200
N= 35
N
N= 200
N= 20
N
Tr'15 Tr
N|Rd|
Tr
0 0.2 0.4 0.6 0.8 1 1.2 1.4
f, [Hz]
10 -4
10 -3
10 -2
10 -1
f, [Hz]
A.
0.2 0.25 0.3 0.35 0.4 0.45 0.5
f, [Hz]
0
0.2
0.4
0.6
S, [m2s]
B.
Equidistant
Cosine stretching
f f
fL= 0.03 fU= 1.4Tp= 3 N= 200 N= 35
Hm0= 4m0Tm01 =m0/m1
Tm02 =pm0/m2Tm10 =m1/m0N
mii
mi=Z
0
fiS(f)f
N
N= 10,000
N= 10,000
N
N
t= 0.02 Te= 5,000
TrTr= 730 N= 1,000
N
N N = 100
0.1%
N= 100
0 20 40 60 80 100
-1
-0.5
0
0.5
1
η, [m]
A.
0 20 40 60 80 100
t, [s]
-1
-0.5
0
0.5
1
η, [m]
B.
0 10 20 30 40 50
-1
0
1
R, [-]
A.
0 100 200 300 400 500
t, [s]
-1
0
1
R, [-]
B.
σ σ
10 110 210 310 4
0.98
1
1.02
Rel. Hm0, [-]
A.
10 110 210 310 4
0.98
1
1.02
Rel. Tm01, [-]
B.
10 110 210 310 4
0.98
1
1.02
Rel. Tm02, [-]
C.
10 110 210 310 4
N, [-]
0.98
1
1.02
Rel. Tm10, [-]
D.
Equidistant
Cosine stretching
N
N= 10,000
η=η0+
N
X
n=1
ancos(ωntkn·x+φn)
η η0N ω
tk x φ
η=η0+
N
X
n=1
an[cos(ωnt+φn) cos kn·xsin(ωnt+φn) sin kn·x]
02468
10 -4
10 -2
10 0
Exceedance
Equidistant
N= 100
02468
10 -4
10 -2
10 0
Exceedance
N= 200
02468
10 -4
10 -2
10 0
Exceedance
N= 500
02468
(H/Hrms)2, (T /Tp)2, [-]
10 -4
10 -2
10 0
Exceedance
N= 1000
02468
10 -4
10 -2
10 0Cosine stretching
N= 100
02468
10 -4
10 -2
10 0
N= 200
02468
10 -4
10 -2
10 0
N= 500
02468
(H/Hrms)2, (T /Tp)2, [-]
10 -4
10 -2
10 0
N= 1000
Rayleigh
Wave height
Wave period
(H/Hrms )2(T/Tp)2
±σ
x
t
2N
z
t x y
x y z
(x, y)z
N= 1
N= 100
10 010 110 210 310 4
10 0
10 1
10 2
10 3
TN/TN=1, [-]
A.
Direct method
Split method
10 010 110 210 310 4
N, [-]
0
10
20
30
Direct over split, [-]
B.
N= 1
5
N= 100 N= 1,000
N2
ResearchGate has not been able to resolve any citations for this publication.
Conference Paper
Full-text available
A 2D RANS-VOF model is used to simulate the flow and sand transport for two different full-scale laboratory experiments: i) non-breaking waves over a horizontal sand bed (Schretlen et al., 2011) and ii) plunging breaking waves over a barred mobile bed profile (Van der Zanden et al., 2016). For the first time, the model is not only tested and validated in terms of water surface and outer flow hydrodynamics, but also in terms of wave boundary layer processes and sediment concentration patterns. It is shown that the model is capable of reproducing the outer flow (mean currents and turbulence patterns) as well as the spatial and temporal development of the wave boundary layer. The simulations of sediment concentration distributions across the breaking zone show the relevance of accounting for turbulence effects on computing suspended sediment pick-up from the bed.
Thesis
Full-text available
The present thesis considers a coupled modelling approach for hydro- and morphodynamics in the surf zone, which is based on a solution to the Reynolds Averaged Navier-Stokes (RANS) equation with a Volume of Fluid (VOF) closure for the surface tracking. The basis for the numerical approach is the surface tracking method in the open-source CFD toolbox OpenFoam(R), which is released by OpenCFD(R). This basic version has been extended with the ability for modelling surface water waves and sediment transport in the surf zone. The validation of these functionalities are described as part of the project. The inequilibrium in the sediment transport field leads to a morphological change in the bed level, which is incorporated through a movement of the computational mesh. This allows for an integrated coupling with the hydrodynamics. The morphological module is also developed as part of this work. The numerical model is applied onto several physical settings. Firstly, the morphological response is turned off, and the hydrodynamics and the sediment transport patterns in the surf zone are described. The description considers these processes as a function of several non-dimensional variables, namely the surf similarity parameter, zeta0, the Dean's parameter in various forms, Omega and OmegaHK. This investigation has an emphasis on (i) the spatial and temporal lag-effects in the hydrodynamics and between the hydrodynamics and the sediment transport and (ii) the integrated net cross shore suspended sediment transport flux as a function of either of the variables zeta0, Omega or OmegaHK. Secondly, the bed is allowed to evolve under the influence of the sediment transport processes. The development of breaker bars in both laboratory scale settings and prototype scale settings is considered. The temporal development of the cross shore profile is simulated for several combinations of wave forcing and sediment grain diameters. The variation is described with emphasis on the development of the crest level of the breaker bar, the variation in the bed shear stress on the crest of the breaker bar, and its migration speed. Additionally, a net onshore current over a breaker bar is considered, where this current mimics the presence of a horizontal circulation cell. The development of a breaker bar is described for different values of the net onshore current speed. This description is undertaken with and without a coupling to the morphology.
Article
Full-text available